
import unittest

import numpy as np





def        _a   (		lowerCamelCase,      lowerCamelCase,      lowerCamelCase,      lowerCamelCase = None,      ):
 lowerCamelCase						:      Optional[Any]							     = np.shape(lowerCamelCase_				)
 lowerCamelCase						:      Union[str, Any]							     = np.shape(lowerCamelCase_				)
 lowerCamelCase						:      Dict							     = np.shape(lowerCamelCase_				)

 if shape_a[0] != shape_b[0]:
  lowerCamelCase						:      int							     = (
      '''Expected the same number of rows for A and B. '''
      F'''Instead found A of size {shape_a} and B of size {shape_b}'''
  )
  raise ValueError(lowerCamelCase_				)

 if shape_b[1] != shape_c[1]:
  lowerCamelCase						:      List[Any]							     = (
      '''Expected the same number of columns for B and C. '''
      F'''Instead found B of size {shape_b} and C of size {shape_c}'''
  )
  raise ValueError(lowerCamelCase_				)

 lowerCamelCase						:      Any							     = pseudo_inv
 if a_inv is None:
  try:
   lowerCamelCase						:      Any							     = np.linalg.inv(lowerCamelCase_				)
  except np.linalg.LinAlgError:
   raise ValueError(
       """Input matrix A is not invertible. Cannot compute Schur complement."""				)

 return mat_c - mat_b.T @ a_inv @ mat_b





class 				A__						(      unittest.TestCase):
      def 		UpperCamelCase__				( self ):
       lowerCamelCase						:      Optional[Any]							     = np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]] )
       lowerCamelCase						:      List[Any]							     = np.array([[0, 3], [3, 0], [2, 3]] )
       lowerCamelCase						:      Optional[Any]							     = np.array([[2, 1], [6, 3]] )

       lowerCamelCase						:      Any							     = schur_complement(__UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )

       lowerCamelCase						:      int							     = np.block([[a, b], [b.T, c]] )

       lowerCamelCase						:      List[str]							     = np.linalg.det(__UpperCAmelCase )
       lowerCamelCase						:      int							     = np.linalg.det(__UpperCAmelCase )
       lowerCamelCase						:      Optional[Any]							     = np.linalg.det(__UpperCAmelCase )

       self.assertAlmostEqual(__UpperCAmelCase       ,    det_a * det_s )
      def 		UpperCamelCase__				( self ):
       lowerCamelCase						:      Optional[Any]							     = np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]] )
       lowerCamelCase						:      Any							     = np.array([[0, 3], [3, 0], [2, 3]] )
       lowerCamelCase						:      Optional[Any]							     = np.array([[2, 1], [6, 3]] )

       with self.assertRaises(__UpperCAmelCase ):
        schur_complement(__UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )






      def 		UpperCamelCase__				( self ):
       lowerCamelCase						:      Optional[Any]							     = np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]] )
       lowerCamelCase						:      Optional[Any]							     = np.array([[0, 3], [3, 0], [2, 3]] )
       lowerCamelCase						:      List[Any]							     = np.array([[2, 1, 3], [6, 3, 5]] )

       with self.assertRaises(__UpperCAmelCase ):
        schur_complement(__UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      unittest.main()







import inspect
from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel, VQModel
from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







class 					__lowercase  (						_SCREAMING_SNAKE_CASE				):





							"""simple docstring"""

							def __init__(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       Any:
														super().__init__()
														self.register_modules(vqvae=__UpperCAmelCase    ,						unet=__UpperCAmelCase    ,						scheduler=__UpperCAmelCase						)






							@torch.no_grad()
							def __call__(					self    ,						__UpperCAmelCase = 1    ,						__UpperCAmelCase = None    ,						__UpperCAmelCase = 0.0    ,						__UpperCAmelCase = 50    ,						__UpperCAmelCase = "pil"    ,						__UpperCAmelCase = True    ,						**__UpperCAmelCase    ,						)		->       Union[Tuple, ImagePipelineOutput]:
														A      :					List[Any]      		=					randn_tensor(
														    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)    ,						generator=__UpperCAmelCase    ,						)
														A      :					List[Any]      		=					latents.to(self.device						)

														# scale the initial noise by the standard deviation required by the scheduler
														A      :					Optional[int]      		=					latents * self.scheduler.init_noise_sigma

														self.scheduler.set_timesteps(__UpperCAmelCase						)

														# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
														A      :					str      		=					'''eta''' in set(inspect.signature(self.scheduler.step						).parameters.keys()						)

														A      :					List[str]      		=					{}
														if accepts_eta:
																					A      :					Optional[Any]      		=					eta

														for t in self.progress_bar(self.scheduler.timesteps						):
																					A      :					Any      		=					self.scheduler.scale_model_input(__UpperCAmelCase    ,						__UpperCAmelCase						)
																					# predict the noise residual
																					A      :					Dict      		=					self.unet(__UpperCAmelCase    ,						__UpperCAmelCase						).sample
																					# compute the previous noisy sample x_t -> x_t-1
																					A      :					int      		=					self.scheduler.step(__UpperCAmelCase    ,						__UpperCAmelCase    ,						__UpperCAmelCase    ,						**__UpperCAmelCase						).prev_sample

														# decode the image latents with the VAE
														A      :					str      		=					self.vqvae.decode(__UpperCAmelCase						).sample

														A      :					Tuple      		=					(image / 2 + 0.5).clamp(0    ,						1						)
														A      :					int      		=					image.cpu().permute(0    ,						2    ,						3    ,						1						).numpy()
														if output_type == "pil":
																					A      :					Union[str, Any]      		=					self.numpy_to_pil(__UpperCAmelCase						)

														if not return_dict:
																					return (image,)

														return ImagePipelineOutput(images=__UpperCAmelCase						)






